For each group of three forces below, determine whether the forces in each pair are pulling at right angles to each other.

a. 12 lb, 13 lb, resultant force 19 lb, yes; 15 lb, 36 lb, resultant force 39 lb, yes

b. 12 lb, 13 lb, resultant force 19 lb, no; 15 lb, 36 lb, resultant force 39 lb, yes

c. 12 lb, 13 lb, resultant force 19 lb, yes; 15 lb, 36 lb, resultant force 39 lb, no

d. 12 lb, 13 lb, resultant force 19 lb, no; 15 lb, 36 lb, resultant force 39 lb, no

To condition in which we can justify if the forces are pulling at right angles to each other is that the sum of the squares of the two lesser number should be equal to the square of the third number. 

For the first set: 12 lb, 13lb, 19lb. 

                                             12^2 + 13^2 ≠ 19^2

For the second set: 15 lb, 36 lb, 39 lb

                                             15^2 + 36^2 = 39^2

The first pair of forces do not pull at a right angle while the second do.
Thus, the answer is letter B. 

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